PS - A and B drive a bicycle one by one

[Navneet]

Hi Ron
A and B drive a bicycle one by one (Other one sitting behind) Speed of A is 2km/h and B is 3km/h and average speed for whole journey is 2.5km/h. What is ratio of distance they traveled.
A. 1:3
B. 1:2
C. 1:4
D. 2:3
E. 3:2

Answer is 2:3 (I framed this question on my own)
Here I want to know why ratio of time they traveled is 1:1
In fact If average speed is 2.8 then ratio of distance is 1:6 but again ratio of time is 1:4
Every time ratio of time is
A:B - (Speed of B- Average speed) : (Average Speed - Speed of A).
Though I remembered this, I unable to visualize why this is happening.

[Navneet]

I have tried two methods to visualize ( And didn't get any way out)
1. Thinking of See Saw ( Unsuccessful )
2. I Tried to think it as work rate problem ( Easy to visualize)
A can do 2 units work/day and B 3unit/day
Total work done is ( Say in 10 days by each working alone) = 2.8*10 = 28
Now there will be unique solution for
2*a ( number of day A work) + 3*b ( number of day A work) = 28
Which is 3*8 +2*2 = 28
Still unable to visualize why number of days they work are coming like 1:4
Still puzzled why
A:B - (Work rate of B- Average) : (Average - Work rate of A).

Please help if there is any logical way

[RonPurewal]

i can't tell exactly what you're asking... are you asking what the correct ratio is? or are you asking why it works? or ...?

if you could ask your question in a way that fits into 1-2 lines of text, that would be helpful.

[RonPurewal]

also—if you don't find a certain shortcut intuitive, then it's probably best not to use it.

i.e., if whatever "weighted-average shortcut" doesn't make sense to your intuition, then just go with the normal, non-shortcut way of calculating weighted averages.

[Navneet]

This means some times we need to use school methods to solve problems.

[RonPurewal]

This means some times we need to use school methods to solve problems.

sometimes? of course.

the point of this test is to be flexible. you should try to absorb as many different problem-solving methods as you can.